No replies yet from people who actually know the answer to your question, so I'll bump the thread with a tangent...
I really like L&M stuff, used them for years. That 300 Dual is a cool-looking host, but I'm not sure it would be worth it to try to power boost with a new LED (even double the luminous flux won't look too bright by today's standards, especially for a 2-headed light with a wired battery pack). I'd be tempted to rip out the stock LED and all electronics, and use a flashlight or other components to hack together another use for the host. (I'm thinking something like the internals from an Emisar D1 wired to a 1S3P 18650 battery pack.)
Good luck with the project, keep us posted, and we'll hope for an actual expert to show up here...